Algebras whose right nucleus is a central simple algebra

Pumpluen, Susanne

Abstract

We generalize Amitsur's construction of central simple algebras over a field F which are split by field extensions possessing a derivation with field of constants F to nonassociative algebras: for every central division algebra D over a field F of characteristic zero there exists an infinite-dimensional unital nonassociative algebra whose right nucleus is D and whose left and middle nucleus are a field extension K of F splitting D, where F is algebraically closed in K. We then give a short direct proof that every p-algebra of degree m, which has a purely inseparable splitting field K of degree m and exponent one, is a differential extension of K and cyclic. We obtain finite-dimensional division algebras over a field F of characteristic p > 0 whose right nucleus is a division p-algebra.

Citation

Pumpluen, S. (2018). Algebras whose right nucleus is a central simple algebra. Journal of Pure and Applied Algebra, 222(9), https://doi.org/10.1016/j.jpaa.2017.10.019

• Journal Article Type: Article
• Acceptance Date: Sep 8, 2017
• Online Publication Date: Oct 23, 2017
• Publication Date: Sep 1, 2018
• Deposit Date: Sep 8, 2017
• Publicly Available Date: Oct 24, 2018
• Journal: Journal of Pure and Applied Algebra
• Print ISSN: 0022-4049
• Electronic ISSN: 0022-4049
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 222
• Issue: 9
• DOI: https://doi.org/10.1016/j.jpaa.2017.10.019
• Public URL: https://nottingham-repository.worktribe.com/output/960758
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022404917302566
• Contract Date: Sep 8, 2017